Mr Barclay, who has been a loyal junior member of Mrs May’s government, was a surprise replacement for Dominic Raab, who quit over the draft “divorce” deal. But the role has been downgraded, with Mrs May taking control of final negotiations. Mr Barclay’s job will instead focus on domestic preparations for Brexit, including steering the divisive plans through Parliament. The son of a trade union official father and a civil servant mother, the 42-year-old describes himself as coming from a “working-class Northern background” in Lancashire.

After training as a lawyer, he worked for the Financial Services Authority and was head of anti-money laundering at Barclays before his political career.

He was appointed after Environment Secretary Michael Gove turned down the position and other senior Brexiteers were also said to have rejected offers.

Downing Street declined to say whether the Brexit Secretary post had been offered to anyone else before the North East Cambridgeshire MP, saying only: “He was the Prime Minister’s choice for the job.”

Mr Gove threw Mrs May a lifeline by deciding to remain in the Cabinet after spending Thursday night deliberating on his future.

Speaking outside his department Mr Gove was asked if he had confidence in the Prime Minister and replied: “I absolutely do.”

He added: “I am looking forward to continuing to work with all colleagues in Government and in Parliament to get the best future for Britain.”

Mr Gove’s decision to remain appeared to mark the end of the ministerial exodus.

But Mrs May was far from safe as backbenchers continued to openly discuss plots to oust her.

More worryingly for the Prime Minister, leading Brexiteers that decided to remain in her Cabinet are planning to hold a series of meetings to press for changes in the deal.

The Commons Leader is understood to be working with allies to decide what can be done “to get it in a better place”, a source said.

Ms Mordaunt remained in the Cabinet after intense speculation she was considering quitting.

Mr Fox said he had “full confidence in the Prime Minister” and added “ultimately I hope that across Parliament we’ll recognise that a deal is better than no deal”.

Although the deal is a draft that must be signed off by European leaders at a Brussels summit, Mrs May has made clear she believes it cannot now be changed.

Ms Rudd’s return to Cabinet comes just seven months after she resigned as home secretary for “inadvertently” misleading MPs over targets for removing illegal immigrants.

She replaces Esther McVey in the Work and Pensions brief and will now face the difficult task of ironing out problems with universal credit benefits. Ms Rudd said that taking over at the DWP was “a really important job, helping 20 million people across the country”, saying: “As a one-nation Tory I want to make sure that we really do help everybody across the country.”

Asked whether responsibility for universal credit was a “poisoned chalice”, she replied: “I have seen universal credit do some fantastic things. “In my constituency in Hastings and Rye it really has transformed lives. But I also recognise that there have been some issues with it, some problems with it.

“I see it very much as my job, my role, to make sure that I try to iron out those difficulties so it becomes a force wholly for good.”

Mrs May’s decision to bring in a Remainer as she filled the two Cabinet vacancies left by Brexiteers is expected to infuriate some MPs.

In other appointments Stephen Hammond replaced Mr Barclay in the Department of Health and Social Care, John Penrose was appointed Northern Ireland Minister and Kwasi Kwarteng joined the Brexit department.

Meanwhile more and more Polish citizens living in the UK are considering moving back to their homeland amid ongoing uncertainty over Brexit, the country’s ambassador to the UK has said.

Arkady Rzegocki said he hoped a strong Polish community would remain after Brexit but he acknowledged some Poles were contemplating either a return home or a move to another country.

Mr Rzegocki said he hoped migrants would be welcomed in the UK after it exits the EU as he highlighted the important role they play in the country’s economy.

“I have to say more and more people are thinking about coming back to Poland, some of them are thinking about different countries, different European countries,” he said.

The ambassador said other factors were also motivating decisions to move home, such as the relative strength of Sterling and Polish zloty, economy improvements in Poland, and simply a desire to reconnect with relatives. But he said Brexit uncertainty was having an influence, saying: “For sure uncertainty is not good for the future.

“I am sure as Polish came here during the Second World War and they are part of the society from this time they will be an important part of the British society also in the future.

“Our work and our challenge is to cooperate despite Brexit.

“We focus mostly on the negotiation process but there is life after Brexit – that’s why many people are working hard to make these links as strong as possible also after Brexit.” The ambassador expressed relief that an upsurge in hate crimes against Polish people in the UK in the wake of the 2016 Brexit referendum had not lasted.